* Prove that the associative law does not apply to ->. I.e., prove that
(P_1 -> (P_2 -> P_3)) notLEQV ((P_1 -> P_2) -> P_3).
* Right associating ...
- Work out a simple rule to determine exactly when
(P_1 -> (P_2 -> ( ... (P_{n-1} -> P_n)...)))
is satisfied.
Prove your rule by induction on n.
* Left associating ...
- Work out a simple rule to determine exactly when
(((...(P_1 -> P_2) ...) -> P_{n-1}) -> P_n)
is...
Prove the Makeham’s second law
µx = A + Hx + BCx
Question 2
Prove the Double geometric law
µx = A + BCx + Mnx
Question 3
Prove the Perk’s law
µx =
A + BCx
KCCx + 1 + DCx
where A, B, C, D, H, K, M and n are constants.
The solubility product constant for strontium sulfate is
3.44*10-7. Using the Debye-Hukel limiting law to
estimate activity coefficients,
a. Calculate the solubility
of strontium sulfate in a solution of 0.100 m KCl
b. Calculate the solubility of
strontium sulfate in pure water.
Prove the following T is linear in the following
definitions
(a) T : R3 →R2 is defined by T(x,y,z) = (x−y,2z)
(b) T : R2 →R3 is defined by T(x,y) = (x−y,0,2x+y)
(c) T : P2(R) → P3(R) is defined by T(f(x)) = xf(x)+f(x)